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Teor. Veroyatnost. i Primenen., 1972, Volume 17, Issue 4, Pages 723–732 (Mi tvp4345)  

This article is cited in 6 scientific papers (total in 6 papers)

On an extension of the class of stable distributions

V. M. Kruglov

Moscow

Abstract: Let $\{\xi_n\}$ be a sequence of independent identically distributed random variables. Put
\begin{equation} \eta_{nj}=\frac{1}{b_j}(\xi_1+\xi_2+…+\xi_{nj})\div a_j \tag{1} \end{equation}
and assume that
\begin{equation} n_j<n_{j+1}, \quad \lim_{j\to\infty}\frac{n_{j+1}}{n_j}=r\geq 1, \qquad r<\infty. \tag{2} \end{equation}

In the paper, the class of limit distributions for the variables (1) under the conditions (2) is studied. This class is shown to possess some properties of the class of stable distributions. A general form of the spectral function of distributions from this class is given (Theorem 1).

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English version:
Theory of Probability and its Applications, 1973, 17:4, 685–694

Bibliographic databases:

Received: 02.07.1970

Citation: V. M. Kruglov, “On an extension of the class of stable distributions”, Teor. Veroyatnost. i Primenen., 17:4 (1972), 723–732; Theory Probab. Appl., 17:4 (1973), 685–694

Citation in format AMSBIB
\Bibitem{Kru72}
\by V.~M.~Kruglov
\paper On an extension of the class of stable distributions
\jour Teor. Veroyatnost. i Primenen.
\yr 1972
\vol 17
\issue 4
\pages 723--732
\mathnet{http://mi.mathnet.ru/tvp4345}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=314095}
\zmath{https://zbmath.org/?q=an:0279.60035}
\transl
\jour Theory Probab. Appl.
\yr 1973
\vol 17
\issue 4
\pages 685--694
\crossref{https://doi.org/10.1137/1117081}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Csoergo S., “Fourier Analysis of Semistable Distributions”, Acta Appl. Math., 96:1-3 (2007), 159–174  crossref  isi
    2. A. N. Chuprunov, L. P. Terekhova, “An almost sure limit theorem for random sums of independent random variables in the domain of attraction of a semistable law”, Russian Math. (Iz. VUZ), 53:11 (2009), 74–76  mathnet  crossref  mathscinet  zmath
    3. Kevei P., Csoergo S., “Merging of Linear Combinations to Semistable Laws”, J. Theor. Probab., 22:3 (2009), 772–790  crossref  isi
    4. Kevei P., “Merging Asymptotic Expansions for Semistable Random Variables”, Lith. Math. J., 49:1 (2009), 40–54  crossref  isi
    5. Theory Probab. Appl., 56:4 (2011), 621–633  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    6. Fukker G., Gyoerfi L., Kevei P., “Asymptotic behavior of the generalized St. Petersburg sum conditioned on its maximum”, Bernoulli, 22:2 (2016), 1026–1054  crossref  mathscinet  zmath  isi  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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